nderstand numbers, ways of representing numbers, relationships among numbers, and number systems

1.1.1 By the end of first grade, students will recognize, write, and orally express the sequential order of the number system.

Recognize and write numerals from 0-10.

Recognize numerals 0-9

Write and read numerals 0-10

What's that number?

Sit in a circle. Roll a number cube with the numerals (0-9) on them. Identify the number rolled.

Count forward by 1s

Uses the correct sequence of number names when counting orally to 12 (THINKING AND KINDERGARTEN Ð 6)

Say numbers 0-12 orally from memory

Count backward from 10 to 0 by 1s.

Say numbers 10-0 orally from memory

Identify ordinal positions of first, second, third, through tenth.

Ordinality (first, second, third)

Put three different objects or shapes in a line. Tell which object is first, second, and third.

Then tell each student what object to place first, then second, and third. Repeat step two but give the orders backwards and randomly repeating numbers as needed

Order those objects
Put objects in order and tell which is first, second, third.

1.1.2 By the end of first grade, students will demonstrate ways of representing numbers and compare relations among numbers.

One-to-one-correspondence

Matching numbers to objects to accurately count objects to ten

Counts with one-to-one correspondence to at least 6 (THINKING AND KINDERGARTEN - 2)

Begins to connect numerals and number names to the quantities they represent (THINKING AND KINDERGARTEN - 4)

Uses the correct sequence of number names to the quantities they represent (THINKING AND KINDERGARTEN - 5)

Counting Jar Ð (Choice Time, page 32)

Count/touch all objects

Count objects by saying one number for each object.

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Conservation of numbers

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Cardinal (1-20)

Keeps track while counting a set of at least 6 objects.  (THINKING AND KINDERGARTEN - 3)

Counting Jar Ð (Choice Time, page 32)

Count a set of objects and identify the total number after counting.

Roll a number cube (0-10) and make a group with that many objects.

Number Relationships

Counts and compares the quantities in two different sets: numbers of students (THINKING AND KINDERGARTEN Ð 11)

TodayÕs Question (Thinking, page 52)

Sequence those trays

Draw a card that has the numeral and dots to match from 0-10. Put a matching amount of objects on a tray. Repeat for several trays and then put the trays in order.

1.1.3 By the end of first grade, students will identify numbers and applications in everyday situations.

Recognize quantities from 0 - 10 with the use of patterns.

Identify how numbers are used in counting situations (setting the table and passing out treats).

Identify how numbers are used for identification (room numbers and phone numbers).

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Identify how numerals are used in the world (Identification and counting).

Use the book Numbers at Play by Charles Sullivan and locate numerals in the pictures.

Take a walk around the school and community and look for numerals. (ex. streets, houses, signs, etc.) tell how they are used. Draw a picture where you saw numerals used and stamp the appropriate numerals on the picture

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Identify equal parts

Give students pictures of shapes that are divided equally and not equally and have them circle the equally divided shapes.

Give students a sheet of paper with the outline of shapes (square, circle, rectangle) and ask them to divide them into two equal parts or halves.

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Identify one-half

Use two whole graham crackers and three sheets of different colored construction paper (red, yellow, and green). Place one graham cracker on the red sheet, 1/2 on the yellow, and 1/2 on the green.

Use construction paper shapes and identify one half for each whole.

Recognize and demonstrate the value of a collection of pennies, nickels, dimes, and quarters whose total value is 100 cents or less.

Identify penny, nickel, dime, and quarter

Pull one of four coins from a sack and identify each coin by name (penny, nickel, dime, and quarter).

1.1.4 By the end of first grade, students will demonstrate the value of numbers (0-20) using concrete objects.

Must be able to do this to do 1.1.2 - relationships. See references in that section.

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Assessment Master 3 Collecting, Counting, and Measuring

2.      Recognizes numerals and number names, 0-10 ((COLLECTING, COUNTING, AND MEASURING))

3.      Connects numerals to the quantities they represent, 0-10 ((COLLECTING, COUNTING, AND MEASURING))

4.      Uses the correct sequence of numbers when counting orally up to 20 ((COLLECTING, COUNTING, AND MEASURING))

5.      Creates a set of a given size, using from 5 to 12 objects ((COLLECTING, COUNTING, AND MEASURING))

6.      Uses an accurate strategy for counting, a strategy that includes one-to-one correspondence, and can keep track of quantities of up to 12 objects ((COLLECTING, COUNTING, AND MEASURING))

7.      Records and represents quantities using objects, pictures, numbers, and/or words ((COLLECTING, COUNTING, AND MEASURING))

8.      Recognizes length as an attribute of an object ((COLLECTING, COUNTING, AND MEASURING))

9.      Measures length by direct comparison ((COLLECTING, COUNTING, AND MEASURING))

10.    Uses language to describe and compare lengths, longer thank shorter than, and the same as ((COLLECTING, COUNTING, AND MEASURING))

11.    Compares two quantities up to 10 and can identify which quantity is more and which is less ((COLLECTING, COUNTING, AND MEASURING))

12.    Uses language to describe and compare amounts, less, lest, more, most, same, equal ((COLLECTING, COUNTING, AND MEASURING))

13.    Orders quantities form least to most and from most to least ((COLLECTING, COUNTING, AND MEASURING))

14.    Finds the total of two single-digit numbers ((COLLECTING, COUNTING, AND MEASURING))

15.    Keeps track of the size of a growing collection of up to 10 objects ((COLLECTING, COUNTING, AND MEASURING))

16.    Finds and records different ways to arrange a set of 6 objects ((COLLECTING, COUNTING, AND MEASURING))

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Assessment Master 4

2.      Has a strategy for accurately counting up to 20 objects (AM-4)

3.      Recognizes situations of one-to-one correspondence (AM-4)

4.      Recognizes situations  of two-to-one correspondence, number of eyes, number of people in pairs (AM-4)

5.      Identifies and describes attributes, physical, functional, of objects (AM-4)

6.      Identifies similarities and differences when comparing objects (AM-4)

7.      Sorts a collection of objects according to one attribute (AM-4)

8.      Sorts a collection of objects in multiple ways (AM-4)

9.      Uses counting to collect data (AM-4)

10.    Describes categories for sorting (AM-4)

11.    Represents data using: concrete materials, pictures, labels or words, and numbers (AM-4)

12.    Observes and describes different representations of the same data (AM-4)

13.    Makes sense of data representations, explains, interprets, and presents (AM-4)

14.    Composes yes/no survey questions (AM-4)

15.    Collects, records, and shares yes/no survey data (AM-4)

16.    Compares sizes of different groups (AM-4)

Solves a mathematical problem based on data (AM-4)

1.2 Computation/Estimation

1.2.1 By the end of first grade, students will demonstrate the concepts of addition and subtraction up to 10.

Demonstrate the value of basic facts using concrete objects.

Recognize the symbols + and - as representing the operations of addition and subtraction.

Recognize the symbol = represents equal quantities.

Solve problems involving one-step solutions related to childrenÕs experiences.

Demonstrate strategies for whole number computation.

Compute efficiently and accurately basic number facts for addition and subtraction

Assessment Master 6

1.      Counts a set of up to 20 objects accurately; demonstrates understanding of one-to-one correspondence, keeps track of the count, and double-checks the total (AM-6)

2.      Compares two quantities up to 20 and can identify which quantity is more and which is less (AM-6)

3.      Keeps track of the size of a growing collection of up to 15 objects (AM-6)

4.      Records and represents quantities using pictures, numbers, and/or words (AM-6)

5.      Repeats a nonstandard unit, a craft stick to measure a length up to 3 units long (AM-6)

6.      Records and represents measurements using pictures, numbers, and/or words (AM-6)

7.      Describes and compares lengths, longer than, shorter than, the same as (AM-6)

8.      Describes and compares quantities, less, least, more, most, same, equal (AM-6)

9.      Describes the positions of objects and the spatial relationships among objects in an arrangement (AM-6)

10.    Uses numbers to describe arrangements of objects and to record how many in all (AM-6)

11.    Is familiar with number combinations totaling up to 6 (AM-6)

12.    Makes sense of combining and separating stories by acting out and retelling the stories (AM-6)

13.    Models number stories and number combinations using objects (AM-6)

14.    Develops strategies for solving combining and separating stories (AM-6)

15.    Finds the total of two quantities up to 12 (AM-6)

16.    Records and represents problems solutions, strategies, and number combinations using pictures, numbers, and/or words (AM-6)

Recognizes that some problems have more than one solution each (AM-6)

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Recognize two quantities from 0 - 10 and their sum with the use of patterns (two red dots and three green dots have the same pattern as five black dots).

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Model addition and subtraction for sums to 10 from memorized patterns or by counting manipulatives to solve problems told to them orally (if we take the two bears on this table and put them with the two bears on that table, how many bears will be on that table?).

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Understand meanings of operations and how they related to one another

Compute fluently and make reasonable estimates

1.2.2 By the end of first grade, students will justify estimations to mathematical problems.

Make estimations and comparisons to actual results.

Understand measurable attributes of objects and the units, systems, and processes of measurement

1.3.1 By the end of first grade, students will measure two or more items or sets using nonstandard units of measure and compare attributes.

Identify purpose of clocks

Explain why people use clocks.

Apply appropriate techniques, tools, and formulas to determine measurements

1.3.2 By the end of first grade, students will identify tools of measurement and their appropriate use (clocks, calendar, ruler, balance scale, and thermometer).

Identify numbers on clocks

Identify the numbers on the clock.

1.3.3 By the end of first grade, students will tell time to the half-hour using an analog and digital clock.

Put numbers in order on a clock

The class will make a large clock on the floor. Each student will put a number where it would go on the clock.

1.3.4 By the end of first grade, students will identify the different units of measurement used in their environment (cents, dollars, pounds, gallons, liters, meters, miles, minutes, and hours).

Identify times of day and length of different time periods.

Ask what events are at certain times of the day (eg.; what do we do at 7:00 in the morning, 12:00 in the day, and 8:00 at night.

Ask what times are morning and night.

Ask what is something that takes about a minute, hour, half-hour, day, week, month, year.

1.3.5 By the end of first grade, students will identify past, present, and future as orientations in time.

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Demonstrate understanding of time (earlier and later)

Ask questions like what comes earlier, and what comes later, assuming they are on the same day (breakfast or lunch, 7:00 in the morning or 7:00 at night, 8:00 in morning or 11:00 in the morning, 11:00 in the morning or 3:00 in  the afternoon).

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Identify the purpose of calendars.

Identify the numbers on a calendar.

Match events with appropriate days of the week

Identify months with climate and special events

Becomes familiar with units of time represented on a calendar: days, weeks, and months (THINKING AND KINDERGARTEN - 8)

Calendar (Choice Time, page 42)

Explain how people use a calendar?

Locate and place numbers on a calendar.

Identify events that happen on days of the week (PE, Music, Art, scout meetings, always order pizza).

Identify at least one month in each of the seasons (summer, winter, spring, fall) and know at least the month for two events (POW-WOW, birthday, Christmas, Hanukah, Thanksgiving, super bowl, É)

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Recognize one cup as a unit of measure.

Identify a one cup container among several different sized containers using a measuring cup as a point  of reference.

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Compare 2 or more objects regarding height, weight, and length

Trace studentsÕ body outlines on large paper. Cut out the body outlines. Fasten them on the wall. Compare the heights of bodies and lengths of different pairs of body parts.

Compare the weight of different objects by identifying the heavier and lighter of different pairs of objects that are easily differentiatde by holding.

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Identify the purpose of thermometers.

Distinguish between hot, medium, and cold temperatures

90's + F as hot

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Explain why and where thermometers are used. (outside, interior, body, food).

Identify temperatures below 40 degrees (F)ahrenheit as cold temperatures in 70 F as nice or room temperature, and

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

1.4.1 By the end of first grade, students will compare relative position (left/right, above/below, over/under, up/down, and near/far).

Specify locations and describe spatial relationships using coordinate geometry and other representational systems

1.4.2 By the end of first grade, students will identify, describe, and create circles, squares, triangles, and rectangles.

Apply transformations and use symmetry to analyze mathematical situations

Use visualization, spatial reasoning, and geometric modeling to solve problems

Recognize spatial concepts of left/right, above/below, over/under, near/far.

Place an object of their choice to match the verbal direction of left, right, above, below, over, under, near and far relative to their body.

Move an object to match the verbal direction of left, right, above, below, over, under, near and far relative to their body

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Recognize a simple pattern in the environment.

Create a simple pattern.

Identify patterns in the school (tiles on floor, carpet patterns, designs on the wall, clothes, etc.)

Design a wallpaper pattern.

Construct congruent shapes and designs using manipulatives.

Identify and describe common geometric shapes in their environment

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Identify circles, squares triangles, and rectangles

Explores and describes geometric shapes (THINKING AND KINDERGARTEN - 9)

(Describe for K equals identify)

Geoblocks (Thinking, page 16)

Use informal language to describe square, triangle and rectangle

Identify each shape (circle, square, triangle, and rectangle).

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Construct congruent shapes and designs using manipulatives

Copy shapes (circle, square, triangle, or rectangle) drawn by another person.

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Name properties (number of sides, and sides of equal length) of shapes (circle, square, triangle, or rectangle).

Identify each shape (circle, square, triangle, or rectangle) and tell how many sides each has, and which sides are the same size.

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Assessment Master 5

2.      Observes and describes 2_D shapes as wholes (AM-5)

3.      Becomes familiar with mathematical vocabulary to describe and name 2-D shapes (AM-5)

4.      Observes and describes attributes of 2-E shapes, including parts of the shapes (AM-5)

5.      Constructs 2-D shapes, coordinates parts to make a whole (AM-5)

6.      Uses shapes to create pictures (AM-5)

7.      Relates 2-D shapes to real-world objects (AM-5)

8.      Combines 2-D shapes to form larger 2-D shapes (AM-5)

9.      Finds combinations of shapes to fill an area (AM-5)

10.    Visualizes and selects shapes to fill a design (AM-5)

11.    Visualizes turning and moving a shape to fit a given space (AM-5)

12.    Explores relationships among pattern blocks (AM-5)

13.    Analyzes visual images, using a strategy for describing, remembering, and replicating those images (AM-5)

14.    Describes the positions of shapes or objects and the spatial relationships among them (AM-5)

15.    Recognizes 3-D shapes in the environment (AM-5)

16.    Observes and describes 3-D shapes as wholes (AM-5)

17.    Observes and describes attributes of 3-D shapes, including parts of the shapes (AM-5)

18.    Becomes familiar with mathematical vocabulary, face, edge, for describing 3-D shapes (AM-5)

19.    Puts 3-D shapes together to make other shapes (AM-5)

20.    Relates a 3-D shape to a 2-D representation of that shape (AM-5)

21.    Observes similarities and differences between the faces of 3-D shapes (AM-5)

22.    Matches a 3-D block to a 2-D outline of one of its faces (AM-5)

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

1.5.1 By the end of first grade, students will collect information about objects and events in their environment (favorite candy bar, number of siblings, and number of pets).

Describes data represented on a graph (THINKING AND KINDERGARTEN - 10)

TodayÕs Question (Thinking, page 52)

Select and use appropriate statistical methods to analyze data

1.5.2 By the end of first grade, students will organize and display collected information using objects and pictures.

Develop and evaluate inferences and predictions that are based on data

1.5.3 By the end of first grade, students will compare and interpret information from displayed data (more, less, and fewer).

Understand and apply basic concepts of probability

1.5.4 By the end of first grade, students will describe the process used in data collection and analysis.

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Sort and classify objects according to one attribute and lay them end to end to make a real-life bar graph.

Recognize that a graph is a good way to see relationships easily.

Create a simple pattern.

Explores the following materials and their attributes: color tiles, pattern blocks, Geoblocks, interlocking cubes (THINKING AND KINDERGARTEN - 1)

Recognize a simple pattern in the environment.

Identify patterns in the school (tiles on floor, carpet patterns, designs on the wall, clothes, etc.)

Design a wallpaper pattern.

Understand patterns, relations, and functions

Represent and analyze mathematical situations and structures using algebraic symbols

Use mathematical models to represent and understand quantitative relationships

Analyze change in various contexts

Assessment Master 2 Pattern Trains and Hopscotch Paths

2.      Observes and describes attributes of objects and sets of objects, such as: size, color, shape, and quantity (AM-2)

3.      Recognizes and  describes a repeating pattern; discriminates between a pattern and a random arrangement or design (AM-2)

4.      Decides which attribute to focus on when constructing a pattern (AM-2)

5.      Copies, constructs, and extends patterns, such as ab, aabb, and aab (AM-2)

6.      Records a pattern (AM-2)

7.      Predicts and verifies what comes next in a pattern (AM-2)

8.      Begins to identify and construct the unit of a pattern, the element that repeats (AM-2)

9.      Begins to decomposes patterns into their units (AM-2)

10.    Adds units to continue a pattern (AM-2)

11.    Begins to make and compare patterns that use the same unit structure, recognizes similarities among several different kinds of ab patterns) (AM-2)

12.    Constructs and extends patterns that grow, or shrink, in predictable ways (AM-2)

13.    Defines a "rule" for how a pattern grows, or shrinks (AM-2)

14.    Creates, represents, and interprets patterns of physical movements, such as hopping or jumping (AM-2)

15.    Constructs a linear pattern in a rectangular frame (AM-2)